n-Fold Cyclic Branched Covers and Overtwisted Contact Structures

2023/08/10 by Jose Ceniceros, Ceniceros, Jose
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2308.05703

openalex publication_date 2023/08/10 · openalex created_date 2023/08/12 · openalex updated_date 2026/07/28

Abstract

This article presents an alternate way to prove a result originally proven by Harvey, Kawamuro, and Plamenvskaya in \citeHaKaPl. We accomplish this by explicitly constructing an overtwisted disk in the p-fold cyclic branched cover of S³ with the standard contact structure branched along a carefully selected transverse knot. Furthermore, by utilizing this construction of the overtwisted disk, we can see that the overtwisted disk is contained in the complement of the branch locus.

Related

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• Cyclic branched covers of alternating knots
• Branched covers of tangles in three-balls
• On geography of symplectic fillings of contact branched covers
• On the strong orderability of overtwisted 3-folds